of Air under Volume and under Pressure. ^^7 



tioned above, the same in both terms, are omitted, as also the 

 constant linear degree of the common- scale. 



Let the temperature be reckoned on 

 AB, as on the common ^cale of an air- 

 thermometer commencing at A or — 

 448° F ; and let CF be a line of such 

 a nature, that every ordinate as BC, 

 EF, &c. may be proportional to the 

 specific heat of air under a constant 



volume, at the respective temperatures B, E, &c. So that the 

 intercepted areas will denote the corresponding variations in 

 the quantity of heat under a constant volume. But if the spe- 

 cific heat of air under a constant pressure exceed that under a 

 constant volume, in the constant ratio of K to 1, and if these 

 ordinates be every where increased in that ratio, another line 

 GD, passing through their extremities, must be of the same na- 

 ture with CF, and the intercepted areas to the former as K to 1. 



Again, let the specific heat of a mass of air under a constant 

 pressure be BD x 1° ; and let its temperature be raised from B 

 to E under the same pressure ; then the area BDGE will denote 

 the increase of heat, and EG X 1 the specific heat under a con- 

 stant pressure at the temperature E. Now EG : EF : : K : 1, 

 wherefore EF x 1° is the specific heat of the dilated mass at the 

 temperature E, under a constant volume. But EF x 1° would 

 still have been the specific heat, had the air under its original 

 volume been raised to the temperature E ; and because EF : 

 EG : : 1 : K, its specific heat at the temperature E under a con- 

 stant pressure would have been EG x 1°, as before. Hence, 

 the constant ratio of the specific heats renders them independent 



of the actual density or pressure, and, therefore -p and ~- 



are constant quantities. It thus appears, that the above ex- 

 pressions for the specific heats answering to a degree on the com- 

 mon scale, vary inversely as \ -\- a t:, or, that any ordinate 

 BD, or BC is inversely as AB, which is the well known pro- 

 perty of the hyperbola ; and, therefore, CF and DG are both 

 hyperbolas, having A for their centre, and AE for an asymptote. 

 We have, then, without going through the process of integrat- 



